Musings on economics and politics, with a special interest in free banking and monetary disequilibrium.

Saturday, May 5, 2012

Nominal GDP Targeting and Shifts in Demand

How do various monetary regimes perform when there is a shift in demand between two goods?

Consider an economy with ten goods. The demand for cotton rises and the demand for burgers falls. If the prices of both goods are perfectly flexible, and assuming the supply and demand curves have the usual shapes, the price of cotton rises and the price of burgers falls. The quantity of cotton rises and the quantity of burgers falls. There is little or no impact on the price level or aggregate real output.

If the reason for spending less on burgers was to be able to spend more on cotton, then it is reasonable to assume total spending has not changed at all. This implies an unchanged nominal income. With the price level more or less unchanged, real income is unchanged along with real output.

Suppose that the supplies of both cotton and burgers are more elastic in the long run than in the short run. As time passes, the initial changes in the prices of the two goods are at least partially reversed, while the changes in the quantities grow. Since the prices and the quantities moves in opposite directions for each good, the effects on spending for each good is ambiguous, but likely to be small as is the effect on total spending. With the price of cotton rising and the price of burgers falling, partly reversing the initial change, there is little effect on the price level.

Now suppose that the supply of cotton is inelastic in the short run, but the supply of burgers if very elastic. While the cotton farmers earn greater profits due to the higher prices and would like to expand production, it takes time to obtain the necessary machinery, hire and train workers, and so on. On the other hand, the burger industry can quickly close down marginal stores and lay off workers. In effect, the price of cotton appears flexible in an upward direction and the price of burgers appears sticky in the downward direction.

With these assumptions about the elasticities of supply, the price of cotton rises a lot, and the price of burgers falls just a little. The price level is higher. Further, the large decrease in the quantity of burgers, evaluated at nearly unchanged prices, is a large decrease in real output. And while the increased spending on cotton may exactly match the decreased spending on burgers, deflating the greater nominal value of cotton by the higher price suggests only a small increase in the real production of cotton.

The shift in the demand away from a good with an elastic supply and towards a good with an inelastic supply results in a higher price level and a lower level of real output. As time passes, the elasticity of supply for burgers might rise even more, but there is little room for change. On the other hand, the great transitory profits for cotton production provides a signal and creates an incentive for an expansion of production. Supply becomes more elastic in the long run. And so, as time passes, the price of cotton falls and its production rises, while the price and production of burgers change little. Therefore, the price level falls back towards its initial value and real output rises back up to its initial value. Because cotton prices are falling at the same time cotton production is rising, the effect of this long run adjustment of spending on cotton and also of total spending is ambiguous, but likely small.

Clearly there are many second order effects of these changes. The supplies of subsittutes in production for cotton fall. The demands for cotton substitutes also make adjustments--rising then falling. The demand for resources used in cotton production rise and so does their prices. The demands for resources used in burger production falls. Presumably the demands for complements for burgers fall. The slight transitional change in real income would impact the demands for luxuries and necessities in a different fashon. Still, it is likely that the largest effect would be on the prices of cotton and closely related products.

I have managed to do this two-sided micro analysis with no assumption about the monetary regime. (I did the same with the initial analysis of the cotton blight.) I wonder how many other economists, particularly with a micro approach, would do the same? It is, of course, unrealistic. Somehow this simple shift in demand between two goods is done with some implicit monetary regime in the background.

Suppose that one of the other eight goods, call it gold, serves as medium of account. The dollar is defined as a fixed amount of gold. This regime appears consistent with the analysis above. The price of burgers fell relative to the price of gold and the price of cotton rose relative to the price of gold. There is no particular reason to expect that the price of gold relative to the prices of any other the other of the seven goods changed much. In the scenario where the supply of burgers was elastic in the short run and the supply of cotton inelastic in the short run, then real output and real income decreased. If gold is a normal good, this would reduce the demand for gold, but the same would be true of all normal goods, and the price of gold, like all the other goods, did fall relative to the price of cotton.

If gold serves as medium of exchange, in the initial scenario, the price level and real output remained unchanged. There was no change in the real demand to hold money or the real quantity of money. There is no reason to expect monetary disequilibrium.

In the second scenario, where the price level increased, because the price of cotton rose more than the price of burgers fell, this would reduce the real quantity of money. However, the reduction in real output and real income would reduce the real demand to hold money. No shortage of money would develop that would prevent the temporary increase in the price level. Further, as the production of cotton adjusts in the long run due to the growing elasticity of supply over time, the lower price of cotton and higher quantity cotton implies a lower price level and higher level of real income. The real quantity of money rises, but the real demand for money rises as well.

Suppose that instead of some "third good," like gold, cotton served as medium of account. With the the dollar price of cotton fixed by definition, the increase in the demand for cotton cannot raise its dollar price. But with an increase in demand, and particularly in the scenario with an inelastic short run supply, the relative price of cotton must rise. This can only occur by a decrease in the dollar prices of the other nine goods. While a Walrasian auctioneer could manage this easily, in a decentralized market economy, the signal to those selling the other nine goods would be fewer sales at existing prices. The burger market, already suffering lower demand, would be hit again, but more importantly, other markets, that are not directly related to the change, would have to make adjustments in their prices because of the shift in demand between burgers and cotton. Of course, as the long run adjustment in the quantity of cotton occurs due to the greater long run elasticity of supply, the relative price of cotton would again fall, requiring an increase in the prices of other goods. The increase in the demand for cotton, when cotton serves as medium of account, results in first a perhaps sharp deflation, and then an inflation as the production of cotton makes its long run adjustment.

While the second order effects of these adjustmetns would impact many markets, and prehaps the market for every other good, it is hardly likely that the decrease in demand for those other goods would accurately signal a need to cut back the production of all of them. While the production of burgers most certainly needs to be reduced due to the lower demand, freeing up resources to produce more cotton, any adjustments in the optimal production of the other goods is ambigous and almost certainly not a decrease in all of them. At first pass, the production of those goods best that can best absorb the resources freed up by the contraction of the burger industry should expand, while the production of those industries with resources that can also be used to produce cotton should contract.

Interestingly, if burgers served as medium of account, and the supply of burgers was highly elastic, then a decrease in demand would require only a slightly lower relative price and so only a slight inflation in the prices of the other goods The price of cotton, however, would still rise sharply due to the difficulty of expanding production quickly, and then fall. This doesn't necessarily mean that burgers would be the ideal medium of account. It isn't obvious that if there were an increase in the demand for burgers, production could be ramped up quickly.

If gold served as medium of account, shifts in the demand between other goods, like cotton and burgers, could result in short run changes in the price level and real output. On the other hands, shifts in the demand between other goods and gold would likely cause very sharp changes in the price level and real output. An increase in the demand for gold would result in deflation, and given the nature of gold production, only a very slow adjustment in long run production. Further, given the large stock of gold relative to current production, a decrease in the demand for gold would not have an effect like burgers, but rather would be be highly inflationary, though the price level should settle at a higher level.

Suppose a fiat currency is used instead some good like gold to serve as medium of account and medium of exchange. If there was an increase in the demand for cotton and decrease in the demand for burgers, the effects would be much the same as if gold served as medium of account and medium of exchange. In the first scenario, there is little or no effect on the price level and so the real quantity of the fiat currency would be unchanged. With real output and real income unchanged, there would be little impact on the demand for the fiat currency.

In the second scenario, in the short run, the price level increases due to the significantly higher price of cotton and only slight decrease in the price of burgers. The real quantity of the fiat currency would fall. However, because of the reduction of real output and real income, the real demand to hold money would fall as well. There would be no shortage of money preventing the temporary increase in the price level. And, as cotton production expands and the price of cotton falls again, the real demand to hold the fiat currency would rise with real income as the real quantity of the fiat currency rose with the lower price level. A fiat currency with a fixed quantity would not prevent temproary changes in the price level due to a shift in demand between goods.

Unfortunately, if the real demand for the fiat currency should change and the quantity remains fixed, then the result is similar to the effects of an increase in the demand for cotton when it serves as medium of account. It would be almost exactly the same as the effects of a change in the demand for gold when it serves as medium of account. Fortunately, the quantity of a fiat currency can be adjusted according to changes in demand.

Since shortages or surpluses of money lead to changes in the price level, it would seem plausible that maintaining a stable price level is the proper rule for its management. However, consider the scenario where the demand for burgers has decreased and the demand for cotton has increased. If the prices are equally flexible, or alternatively, the elasticities of supplies and demands result in offsetting impacts on prices, then the price level would remain unchanged, and the regime of price level stabilization would require no adjustment in the quantity of money.

On the other hand, in the scenario where the supply of cotton was inelastic and the supply of burgers elastic, the price level increased. A regime of maintaining a stable price level would require a decrease in the quantity of money sufficient to force the price level back down. While there would be some slight dampening in the increase in the price of cotton, and perhaps a slightly greater decrease in the price of burgers, the larger effect would be modest decreases in the prices of the other 8 goods in the economy.

As the production of cotton gradually expands, due to supply being more elastic in the long run, the lower price of cotton would result in a lower price level, which would require an expansion in the quantity of money. This would dampen the decreases in the price of cotton, reverse any added decrease in the price of burgers due to the monetary contraction and, most importantly, allow all the prices of the other goods to recover.

To the degree that the other 8 goods respond like burgers, especially to a temporary decrease in demand, a sharp monetary contraction might be needed to reduce their prices enough. Unfortunately, that implies the simultaneous a sharp contraction in the production of all of those other 8 goods.

It is instructive to consider the impact of the monetary contraction on the process by which the quantity of cotton recovers. Without the monetary contraction, the price of cotton rises further and so the profitability is immediately greater. Resources are pulled into the cotton industry, though with the contraction of the burger industry, there is some pushing of resources towards cotton as well. With the monetary contraction, the price of cotton rises less, and so there is a bit less pull, but the rest of the economy contracts more, so there is much more push. In other words, it would be lower resources prices, including wages, that would provide a more significant part of the impetus to expand cotton production. If resource prices, and especially nominal wages, were sticky, there could be very little impetus from that source.

In the limit, suppose that all prices and wages are completely rigid downward. The monetary contraction must be severe enough to prevent the price of cotton from rising, that being the only way to keep the price level from rising. While production and employment in the rest of the economy would fall, there would be no signal to those producing cotton that it is profitable to expand. Fortunately, it is unlikely that prices would all be perfectly rigid, but hopefully considering that extreme scenario illustrates why simply allowing the increase in the price of a good with increased demand to cause a higher price level is the least disruptive approach. Forcing other prices down to keep the price level stable is simply an undesirable disruption in the the adjustment process.

Suppose that nominal GDP is targeted rather than the price level. In the first scenario, the price and quantity of burgers fall and the price and quantity of cotton rises. Even if spending on each good changes, total spending was unchanged. A target for nominal GDP has the same consequence as a target for the price level. There is no monetary change necessary.

In the second scenario, however, where the supply of burgers is elastic in both the short and long run, but the supply of cotton is inelastic in the short run and becomes more elastic over time, there is a difference. Like a gold standard and a fixed quantity of money, a rule for stable nominal GDP requires no monetary change. While the price of burgers falls little, the substantial reduction in the quantity of burgers imply a substantial decrease in spending on burgers. Similarly, while the production of cotton rises little in the short run, the price rises substantially. Spending on cotton rises. While the price level increases, real output decreases, leaving nominal GDP little changed. As the production of cotton expands, and the price falls, there are offsetting impacts on spending on cotton. The lower price level and expansion in real output have an offsetting impact on nominal GDP.

Backward looking inflation targeting would have a similar consequence as nominal GDP targeting. If the increase in the price of cotton is observed, then no effort would be made to reverse it. Unfortunately, forward looking inflation targeting would require a monetary contraction that prevented the shift in demand from causing a higher price level. And, of course, flexible inflation targeting allows the monetary authority to do as they choose. Unfortuately, it appears that this very flexibility creates a motivation to "maintain credibility" and "keep inflation expectations anchored" so that a contractionary monetary policy is implemented when there is a shift in demand between goods.

A rule keeping nominal GDP on target allows those prices of those particular goods with increased demand to rise, generating appropriate signals and incentives for those firms to expand production and employment. As production expands, prices then fall again, returning the price level to its intitial level. Nominal GDP targeting is much superior that stablizing the price level when there is a shift in demand between various goods. Slow, steady growth in spending on output provides the least bad macroeconomic environment for microeconomic adjustment.

1 comment:

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